Although military sources had put the death toll of the Radisson Blu hotel as high as 27, Malian President Ibrahim Boubacar Keita put it at 19, with seven wounded, in a speech to the nation broadcast on national television on Saturday.
"Our forces have courageously managed to limit and neutralise the threat from these fanatics who were fiercely determined to carry out a complete and utter massacre of everything that showed signs of life at the hotel," he said. "Forces from friendly countries, including France, the US and Minusma, contributed to bringing a speedy end to this tragedy, which could have been even bigger."
The attackers had "nothing to do with the religion of Mohammed, a peaceful religion", he went on.
Three suspects are now being sought, a security source told the AFP news agency, without giving further details so as not to compromise the investigation.
The Al-Mourabitoune group of Algerian jihadist Mokhtar Belmokhtar has claimed responsibility for an operation carried out in conjunction with Al-Qaida in the Islamic Maghreb.
An emergency cabinet meeting chaired by Keita declared a 10-day state of emergency to help the search for "terrorists on the run and possible accomplices" and three days of mourning to start on Monday.
Former Tuareg separatists, who allied with Islamist armed groups to take over the north of Mali in 2012 but have accepted a peace deal with the government, condemned the attack.
So did UN Secretary General Ban Ki-moon, French President François Hollande, US President Barack Obama, China's Xi Jinping and Russia's Vladimir Putin, who called for "broad international cooperation" to fight "terrorism".
Russian warplanes carried out the heaviest airstrikes on Islamic State positions in eastern Syria since the war began on Friday, killing at least 36 people in at least 70 strikes.
Six Russians were killed in the hotel attack, Russia's foreign ministry said Saturday.
They were among 12 Russian nationals, all employees of private freight airline Volga-Dnepr, staying at the Radisson Blu.
Three Chinese, two Belgians, an American and a Senegalese were among the dead, according to their own countries.